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15 Nov 2009, 21:47

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If x, y, and z are positive integers, where x > y and z=x^(1/2), are x and y consecutive perfect squares? (A perfect square is defined as the square of an integer. For example, 36 is a perfect square since it equals 6 squared, while 38 is not a perfect square since it is not equal to the square of any integer.)

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16 Nov 2009, 00:27

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ctrlaltdel wrote:

If x, y, and z are positive integers, where x > y and z=x^(1/2), are x and y consecutive perfect squares? (A perfect square is defined as the square of an integer. For example, 36 is a perfect square since it equals 6 squared, while 38 is not a perfect square since it is not equal to the square of any integer.)

(1) x + y = 8z +1(2) x – y = 2z – 1

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1. x+ y = 8z+1the values of x and y satisfying this equation is 25 and 16 which are consecutive perfect squaresthe values of x and y satisfying this equation is 64 and 1 which are NOT consecutive perfect squaresHence insuff

Re: If x, y, and z are positive integers, where x > y and [#permalink]

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26 Sep 2013, 03:00

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Re: If x, y, and z are positive integers, where x > y and [#permalink]

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30 Apr 2015, 18:18

If x, y, and z are positive integers, where x > y and z=x^(1/2), are x and y consecutive perfect squares? (A perfect square is defined as the square of an integer. For example, 36 is a perfect square since it equals 6 squared, while 38 is not a perfect square since it is not equal to the square of any integer.)

Re: If x, y, and z are positive integers, where x > y and [#permalink]

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14 Jul 2016, 09:41

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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